You write custom CUDA kernels to replace the pytorch operators in the given GeGLU architecture to get speedups.

You have complete freedom to choose the set of operators you want to replace. You may make the decision to replace some operators with custom CUDA kernels and leave others unchanged. You may replace multiple operators with custom implementations, consider operator fusion opportunities (combining multiple operators into a single kernel, for example, combining chunk+gelu+elementwise_mul), or algorithmic changes (such as optimized memory access patterns). You are only limited by your imagination.

his CUDA kernel implements optimized Gower distance calculation with the following strategies:

Memory Optimization:

Vectorized memory access using float4 for 4x bandwidth utilization

Read-only cache via __ldg() instruction

Shared memory for storing ranges to avoid global memory access

Contiguous tensor inputs

Parallelization Strategy:

Two kernel variants: batch-per-block for small batches, grid-stride loop for large batches

Warp-level reduction using warp_sum_fast with XOR shuffling

Instruction-Level Parallelism (ILP) with #pragma unroll 2

Dynamic block allocation based on GPU multiprocessor count

Numerical Optimization:

Fast math operations: __frcp_rn() for reciprocal, fabsf() for absolute value

Epsilon stabilization to prevent division by zero

Early clamping of range values

Performance Tuning:

256 threads per block optimal configuration

Shared memory allocation proportional to feature dimension

Compiler flags: -O3, --use_fast_math for aggressive optimization

The implementation efficiently handles both small and large batch sizes while maximizing memory throughput and computational efficiency.


Here's an example to show you the syntax of inline embedding custom CUDA operators in torch: The example given architecture is:
import torch
import torch.nn as nn


class Model(nn.Module):
    def __init__(self, eps=1e-12):
        super().__init__()
        self.eps = eps

    def forward(self, x: torch.Tensor, y: torch.Tensor) -> torch.Tensor:
        combined = torch.cat([x, y], dim=0)
        global_min = combined.min(dim=0).values
        global_max = combined.max(dim=0).values

        ranges = global_max - global_min

        ranges = torch.clamp(ranges, min=self.eps)

        diff = torch.abs(x - y)
        return (diff / ranges).mean(dim=1)


batch_size = 128
feature_dim = 512


def get_inputs():
    x = torch.randn(batch_size, feature_dim, dtype=torch.float32)
    y = torch.randn(batch_size, feature_dim, dtype=torch.float32)
    return [x, y]


def get_init_inputs():
    return [1e-12]